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Turbulent mixing in a Richtmyer–Meshkov unstable light–heavy–light (air–
${\mathrm{SF} }_{6} $
–air) fluid layer subjected to a shock (Mach 1.20) and a reshock (Mach 1.14) is investigated using ensemble statistics obtained from simultaneous velocity–density measurements. The mixing is driven by an unstable array of initially symmetric vortices that induce rapid material mixing and create smaller-scale vortices. After reshock the flow appears to transition to a turbulent (likely three-dimensional) state, at which time our planar measurements are used to probe the developing flow field. The density self-correlation
$b= - \langle \rho v\rangle $
(where
$\rho $
and
$v$
are the fluctuating density and specific volume, respectively) and terms in its evolution equation are directly measured experimentally for the first time. Amongst other things, it is found that production terms in the
$b$
equation are balanced by the dissipation terms, suggesting a form of equilibrium in
$b$
. Simultaneous velocity measurements are used to probe the state of the incipient turbulence. A length-scale analysis suggests that an inertial range is beginning to form, consistent with the onset of a mixing transition. The developing turbulence is observed to reduce non-Boussinesq effects in the flow, which are found to be small over much of the layer after reshock. Second-order two-point structure functions of the density field exhibit a power-law behaviour with a steeper exponent than the standard
$2/ 3$
power found in canonical turbulence. The absence of a significant
$2/ 3$
region is observed to be consistent with the state of the flow, and the emergence of the steeper power-law region is discussed.

The properties of turbulent mixing in a Richtmyer–Meshkov (RM) unstable fluid layer are studied under the impact of a single shock followed by a reshock wave using simultaneous velocity–density measurements to provide new insights into the physics of RM mixing. The experiments were conducted on a varicose fluid layer (heavy fluid) interposed in air (light fluid) inside a horizontal shock tube at an incident Mach number of 1.21 and a reflected reshock Mach number of 1.14. The light–heavy–light fluid layer is observed to develop a nonlinear growth pattern, with no transition to turbulence upon impact by a single shock (up to ). However, upon reshock, enhanced mixing between the heavy and light fluids along with a transition to a turbulent state characterized by the generation of significant turbulent velocity fluctuations () is observed. The streamwise and spanwise root-mean-squared velocity fluctuation statistics show similar trends across the fluid layer after reshock, with no observable preference for the direction of the shock wave motion. The measured streamwise mass flux () shows opposing signs on either side of the density peak within the fluid layer, consistent with the turbulent material transport being driven along the direction of the density gradient. Measurements of three of the six independent components of the general Reynolds stress tensor () show that the self-correlation terms and are similar in magnitude across much of the fluid layer, and much larger than the cross-correlation term . Most importantly, the Reynolds stresses () are dominated by the mean density, cross-velocity product term (), with the mass flux product and triple correlation terms being negligibly smaller in comparison. A lack of homogeneous mixing (and, possibly, a long-term imprint of the initial conditions) is observed in the spanwise turbulent mass flux measurements, with important implications for the simulation and modelling of RM mixing flows.

An experimental investigation of mixing mechanisms in a shock-induced instability flow is described. We obtain quantitative two-dimensional maps of the heavy-gas (SF6) concentration using planar laser-induced fluorescence for the case of a shock-accelerated cylinder of heavy gas in air. The instantaneous scalar dissipation rate, or mixing rate, χ, is estimated experimentally for the first time in this type of flow, and used to identify the regions of most intense post-shock mixing and examine the underlying mechanisms. We observe instability growth in certain regions of the flow beginning at intermediate times. The mixing rate results show that while these unstable regions play a significant role in the mixing process, a large amount of mixing also occurs by mechanisms directly associated with the primary instability, including gradient intensification via the large-scale strain field in a particular non-turbulent region of the flow.

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